c Journal of Applied Mathematics & Decision Sciences, 2(1), 23{50 (1998)
Reprints Available directly from the Editor. Printed in New Zealand.
A DECISION SUPPORT SYSTEM FOR
REGIONAL HAZARDOUS WASTE
MANAGEMENT ALTERNATIVES
MAHYAR A. AMOUZEGAR
m.amouzegar@massey.ac.nz
Institute of Technology & Engineering, SST 4.29, Massey University, New Zealand.
STEPHEN E. JACOBSEN
jacobsen@ee.ucla.edu
Department of Electrical Engineering, University of California, Los Angeles, CA 90024, USA.
Abstract. With the passage of the Resource Conservation and Recovery Act (RCRA), and the
subsequent amendments to RCRA, eorts to provide tighter controls on the transportation and
disposal of hazardous waste have been steadily gaining ground. This paper, intended as a decision
support tool for regional planning, incorporates information on the hazardous waste generation,
treatment capacity and the costs of waste treatment alternatives into an optimization problem
of nding the relationship between governing agency and the toxic waste producing rms. As an
example, we consider the problem of regional hazardous waste in the San Francisco Bay Area in
Northern California.
Keywords: Decision Support System, Hazardous Waste Management, Mathematical Programming, Bilevel Programming.
1. Introduction
Pollution has been an inevitable accompaniment to economic activities, and as such,
most societies have set goals to eliminate, or at least reduce, pollution. It has long
been recognized that industries or rms may not voluntarily reduce pollution levels
in the absence of any government compulsory intervention. Such intervention can
take either of two forms: a) the government can takeover and run some lines of
activity, or b) it can leave the activity to private initiative but regulate it.
Many states generate large amount of hazardous waste for which there is not, at
present, adequate treatment and disposal capacity within the state. Federal and
state legislation requires that management policies provide for adequate long-term
treatment and disposal capacity for such waste. California's policy, for example,
calls for meeting treatment requirements by reducing the generation of hazardous
waste, with expansion of treatment and disposal capacity only as a secondary solution. Within the state, hazardous waste management planning is also being done at
the regional level. Regional governments must project hazardous waste generation
and plan for adequate treatment and disposal capacity in their region. Estimates
of future waste generation are based on population and economic projections, and
then reduced by some percentage across-the-board to account for projected waste
reduction.
24
M. AMOUZEGAR AND S. JACOBSEN
At present, regional planners do not consider the relationship between treatment
capacity, treatment prices and hazardous waste generation. Large o-site treatment
facilities oer economies-of-scale provided that the are fully utilized however, if
the capacity is larger than anticipated demand then the facility could be forced to
increase the unit treatment price which could produce further decrease in demand
and price increases. As a result the facility many be be able to recover costs
or operate only at higher than projected unit prices. The addition of treatment
capacity could also produce other unintended outcomes: low treatment prices could
undermine waste minimization eorts or the facility may utilize excess capacity by
treating wastes from outside the region.
In order to fully understand the fundamental characteristic of hazardous waste
management, we must introduce two important agents in the economy: The central
authority and the rms. The central authority (CA) is dened as any agent in the
economy which has the authority to regulate the other agents' activity.
We dene a rm as any organization that, through its activity produces some
goods, not necessarily identical, in order to maximize its own prot. As a by
product of the rm's activity, hazardous waste is also generated which needs to be
managed.
In this paper, we present an optimization model for hazardous waste capacity
planning and treatment facility location. The behavior of private rms is modeled
to assess the eect of central planning decisions and price signals on hazardous
waste generation and demand for treatment and disposal. In short, we are mainly
concerned with the interaction between the two agents: the CA seeking to regulate
the rms in order to maximize the social welfare and the rms responding to these
regulations. Furthermore, we have focused our attention on a group of wastes
classied as incinerable hazardous wastes since it constitute the largest non-nuclear
waste group in the US.
The management of incinerable wastes are divided into four major categories:
1. Source reduction: The elimination or reduction of waste at the source.
2. Recycling: The recycling or reuse of waste material both on-site and o-site
(regional level). Recycling is not 100%, and some residuals need to be sent for
incineration and disposal.
3. Incineration: Thermal destruction of waste at o-site facilities.
4. Disposal: Releasing material into air, water and land. This option is assumed
to be a joint process with the incineration.
Among all the technique of waste management, source reduction is favored due
to its lower risk to the environment, and thus is the common sense solution to
the prevention of future hazardous waste problems. But due to lack of proper
environmental regulation and/or economic consideration, recycling and incineration
are part of today's waste management options. The latter processes bring with them
DSS FOR REGIONAL HAZARDOUS WASTE MANAGEMENT ALTERNATIVES
25
certain damage (or externalities) to the environment which we will call pollution
damage.
The model, intended as a decision support tool for a regional hazardous waste
management authority, is necessarily a simplication of the actual conditions and
subject to constraints and assumptions which are described below. Still, it provides
a framework for qualitatively comparing the eects of dierent planning options.
2. Scope of Hazardous Waste Problem
More than 60,000 chemicals (excluding pharmaceuticals or pesticides) enter into
many products and services that shape today's lifestyle. Taken together, these
chemicals, comprise a huge industry { in the United States alone, sales during 1995
were over $200 billion. The sheer variety, ubiquity and economic importance of
chemicals means that eective regulation to safeguard against undesirable health or
environmental side eects is quite challenging31]. In California, every year, about
26,000 rms generate and ship o-site over 2.2 million tons of hazardous waste{
more than 150 pounds per person in the state. This represents an increase of over
600,000 tons from the total reported just two years earlier. The rapid production
of hazardous waste combined with increase in disposal cost and decrease in the
available numbers of landll sites, changes in legislation, and more public awareness
have dramatically altered the way in which we can deal with hazardous waste. Prior
to the late 1980's, a detailed accounting of the generation and disposal patterns
for hazardous waste streams was unavailable however, with the data collection
provisions enacted under Superfund reauthorization and the Resource conservation
and Recovery Act (RCRA), the legal authority to collect such data was put in place.
Now there are several data bases which provide partial pictures of hazardous waste
generation and disposal. The Toxic Release Inventory (TRI)41], collected annually
under Superfund Amendment and Reauthorization Act (SARA), Title III, provides
data on the emission proles of more than 300 chemical species. While the TRI data
are useful for proling waste generation patterns, they provide little information on
disposal methods. In contrast, the biennial survey of generators and the biennial
survey of Treatment, Storage and Disposal facilities collected under RCRA, provide
data on disposal patterns but little data beyond waste category on the composition
of the waste streams.
In 1985, Environmental Protection Agency (EPA) conducted the National Screening Survey of Hazardous Waste Treatment, Storage, Disposal and Recycling (TSD)
facilities. The survey was designed to estimate the total quantity of hazardous waste
managed by TSD facilities and to identify hazardous waste management processes.
This survey identied 2,959 facilities, regulated under RCRA, which managed a
total of 247 million tons of waste 43]. An additional 322 million tons of hazardous
waste was handled by units exempt from RCRA reporting requirements.
M. AMOUZEGAR AND S. JACOBSEN
26
2.1. Evolution of State and Federal Regulation
Currently there are 11 major environmental laws for controlling dierent types of
waste generated throughout the country 42]. One of these laws which concerns
hazardous waste, is the Resource Conservation and Recovery Act of 1976 with its
\cradle-to-grave" provisions for controlling the storage, transportation, treatment
and disposal of hazardous waste. RCRA was signicantly amended in 1980 and
1984. The 1984 amendment of RCRA, called Hazardous and Solid Waste Act
(HSWA) is very important in establishing more stringent standards in waste management strategy. These amendments have restricted untreated hazardous waste
from land disposal (\Land Ban")40] and state laws such as Hazardous Waste Management Act of 1986 (SB1500), which augments the federal Land Ban to include
some California-only hazardous wastes. The Land Ban also species hazardous
waste treatment standards, which for many wastes require that specic treatment
technologies be applied. California law further requires that all hazardous waste
containing more than one percent volatile organic compounds or having a heating value of more than 3 000 BTU/lb must either be incinerated or treated by an
equally eective approved process 36].
Planning for hazardous waste treatment and disposal is being done at both the
state and county level. Federal law (CERCLA 104(c)(9)) requires that states, or a
cooperating association of states, prepare Capacity Assurance Plans (CAP) or lose
federal funding for Superfund cleanups in the state. Where there is a shortfall of
treatment and disposal capacity, the state(s) must show that measures are being
taken to meet the shortfall. In California, AB650 has required that the Department
of Toxic Substances Control prepare such a plan in 1989 and revise it every three
years.
Long before the state's rst Capacity Assurance Plan was prepared, the legislature
had recognized that additional facilities were needed, but that siting of such facilities
was meeting strong opposition at the local level. `Hazardous Waste: Management
Plans and Facility Siting Law'37], known as Tanner Act, provided guidelines and
funding for county and regional governments to assess hazardous waste generation
within their jurisdiction and to develop waste management plans to guide future
policy decisions, including the siting of new treatment facilities. The law also set
up a process for evaluating facility siting proposals through a Local Assessment
Committee and a state appeals board.
The legislation allows counties to participate in regional associations for hazardous
waste management planning. The two principle association are the Association of
Bay Area Governments (ABAG), comprised of Alameda, Contra Costa, Marin,
Napa, San Francisco, San Mateo, Santa Clara, Solano and Sonoma counties, and
the Southern California Hazardous Waste Management Authority (SCHWMA),
comprised of Imperial, Los Angeles, Orange, Riverside, San Bernardino, San Diego
and Santa Barbara counties. ABAG and SCHWMA account for approximately
25% and 50%, respectively, of all hazardous waste generation in the state.
x
DSS FOR REGIONAL HAZARDOUS WASTE MANAGEMENT ALTERNATIVES
27
3. A Survey of Pollution Control
A major tenet of this paper is that there are signicant gaps in our understanding of
pollution control and rms' behavior in other than highly abstract economies with
full information assumptions. It is important to recognize our limited knowledge
about the rms' response to regulatory action by the central authority and even
more signicantly, the lack of complete data on hazardous waste generation and
treatment.
In this section, we review past work that can contribute to a better understanding
of subsequent sections. Roughly speaking, the literature includes four broad, and
sometimes overlapping, topical areas: conceptual models, extensions to the earlier
models, eect of uncertainty and optimization methods.
3.1. Conceptual Models
Conceptual models and discussions focusing on eciency gains of market-base approaches compared with command and control has been discussed by many authors
such as Kneese22], Dale8], Baumol and Oats4], and Kneese and Schultz23]. Allen
Kneese22] had the early insights in terms of treating pollution management as an
economic allocation processes in his work on water pollution. His contribution was
to point out that pollution control is not just an engineering problem (which can be
solved by technology), or just a political problem, but it is also an economic allocation problem. His prescription was to utilize pigouvian fee (i.e., emission charge),
to achieve a socially desirable level of pollution.
Following Kneese's work on water pollution, Crocker7] examined air pollution
control as an economic allocation problem. Although his work treats the problem
on a very general level, he does introduce the notion of marketable property right for
the use of air resources. Dale8] expands considerably on the notion of a pollution
permit and property rights.
Although these early works introduced most of the ideas used by today's researchers, it is noticeably decient in the quantitative rigor needed to approach
pollution problems.
3.2. Extensions
Extensions of these models addressing complications such as space (i.e., multiple
regions) and uctuating pollutant disposal. Montgomery32] and Tietenberg39]
have developed general equilibrium model to examine optimal pollution control
focusing on these considerations. Montgomery32] examines marketable permits to
pollute within a spatial economy. His paper is important because it shows that an
equilibrium will exist for a marketable permit system such as proposed by Dale8].
Susan Rose-Ackerman34] pointed out a host of practical problems associated with
emission fees. Some of her criticism have previously surfaced in terms of general
28
M. AMOUZEGAR AND S. JACOBSEN
diculties with the marginalist allocation process. Other perceived problems with
emission fees are merely observation on the diculty of controlling pollution and
are not unique to economic instrument. Therefore, her criticism do not appear
to signicantly weaken the case for emission fees or marketable permits, a case
whose principal interest lies in its alignment of public and private incentives. RoseAckerman suggests two problems: One problems arises when non-constant return
to scale apply to either pollution damage or emissions. In such case, marginal
cost pricing can lead to nonzero prot for producer. A rm may be driven out of
business, or forced to leave the region, if it is forced to pay the emission fee. But
this can be true for any input and there is no indication that economic eciency is
reduced.
A second issue raised by her is the potential ineciencies associated with an
emission fee that is uniform in either space or time. These ineciencies (relative to
a uniform emission standard) associated with uniform fee depend on the curvature
of the cost and benet functions. But once again, it should be pointed out that
fees need not to be uniform.
Finally, Kruppick, et. al. 25] examined the marketable permit system for the
control of air pollution. In their paper, they allowed for free trade of emission
permits subject to the constraint of no violations of the predetermined air quality
standard at any receptor points.
3.3. Eects of Uncertainty Price vs. Quantity]
A number of authors have introduced uncertainty into their analysis and on this
basis have shown the optimality of particular control mechanism. Weitzman45]
has shown under what conditions price instrument are preferred to quantity instruments in centrally allocating production and consumption. He conrmed Lerner's
conjecture(29]) that under uncertainty, the choice between fee and permits will
depends on the slopes of the marginal damage and cost functions. Kolstad24]
explicitly included uncertainty in his empirical model. He examined and compare
three regulatory issues: price control vs. quantity control spatially dierentiated
vs. undierentiated control and command-and-control regulation vs. economic
instrument.
Beavis and Dobbs5] examined the rm behavior under regulatory control with
the assumption of stochastic euent generation. These authors assumed that waste
discharge depends on some input and a continuous random variable with a known
density function.
3.4. Optimization Approach
Many authors have attempted optimization techniques in the pollution abatement
problem (e.g., 30], 15], 17], 14]). Graves, et. al. 15] used a large scale nonlinear
programming in a pollution abatement model for West Fork White River in Indiana
DSS FOR REGIONAL HAZARDOUS WASTE MANAGEMENT ALTERNATIVES
29
in order to minimize the total cost of pollution abatement structure subject to water
quality in each section of the river. Haimes, et. al. 16] and Hass 19] approached
the abatement of water pollution through decomposition techniques of Dantzig
and Wolfe9]. Their goal was to simultaneously compute an optimal waste water
treatment conguration and to determine optimal pollution taxes to achieve this
conguration.
Models of Haime, et. al. 16] and Hass19] depend crucially upon the assumption that the system is i) centralized, and ii) the centralized system is capable of
decentralization. Jacobsen21] showed that once revenue sensitivities and appropriate benet measures are introduced, usually both of the above assumptions do
not hold. Hall and Jacobsen17] highlighted the importance of response functions
due to specic regulatory policies. They developed an optimization model based on
consumers' surplus, prot loss, and changes in tax revenues and concluded that,
when information costs are too high, it is most ecient to tax the solid wastes
directly rather than the tax the goods that produced such wastes.
In most of these models, the solution is derived from a microeconomic approach,
in the sense that it is found by locating the point where the marginal treatment
cost equals to the marginal damage cost from the perspective of a particular individual polluter (some noted exceptions are Jacobsen21], Hall and Jacobsen17],
and Kolstad24]). However, a serious shortcoming of these models is that complete
information on the production and damage cost functions of each and every rm
is assumed to be known. Although, each rm may know its own production cost
functions, there is no reason to believe that this information will be readily available
to the central authority.
Some researcher have conceptualized the problem in terms of a multilevel frame
work 1], 19], 16], 24]. Although Hass19] seemed to realize the existence of two
levels, he did not formulate his model as such. Instead, he modeled the problem as
a single level and solved it by using Dantzig-Wolfe nonlinear decomposition.
Haimes, et. al. 16] also recognized the need to consider the problem from a multilevel modeling viewpoint. They proposed a formulation consisting of three level:
a central authority, a regional treatment plant, and the individual polluter. Their
solution method decomposed the optimization problem into a set of hierarchically
ordered subproblems. The solutions of these subproblems were then coordinated
to obtain an optimal solution to the original problem. More specically, once the
central authority determines the tax schedule, it send this information down to the
lower levels. The lower levels then process the tax structure and pass results back
up to the central authority as optimal treatment levels. Using these treatment levels, the central authority checks the quality constraints to determine if the previous
taxing structure is too high (no binding constraints), too low (some constraint violated), or optimal(no constraints violated, some binding constraint). If the previous
tax structure is not optimal, a new tax structure is developed. The iterative nature
of this solution technique is necessary since there is no mechanism, inherent in the
model, which assumes that central authority has any knowledge of the lower level
optimization problems. The obvious diculty with such iterative tax setting is that
30
M. AMOUZEGAR AND S. JACOBSEN
Table 1. Hazardous Waste Generation in California
1988
1989
In-state generation, HWIS 1,498,258 1,954,829
Exports, based on HWIS
159,834
254,964
Exports, from OSMA
52,009
74,880
Total in-state generation
1,550,267 2,029,709
Total exports
211,843
329,844
1990
2,169,715
292,326
71,841
2,241,556
36,4167
1991
2,145,283
259,521
90,115
2,235,398
349,636
the lower level (rms) assumes the initial taxes are substantially correct, and they
plan their pollution control program which may take several years to complete, and
it is largely irreversible once in place.
Kolstad24] formulated his Four Corner case study in terms of a stochastic bilevel
problem, but his interest was to derive some empirical properties for various air
pollution regulations.
4. Management of Hazardous Waste in California
In the 1989 Capacity Assurance Plan, the state established a goal of managing
California's waste within the state and limiting exports to 1987 levels. While emphasizing waste minimization and source reduction as the preferred way of managing hazardous waste, the plan saw a need for additional treatment capacity for
incineration of liquids, sludges and solids, and projected that several new incineration facilities would be built. However, all proposals for incineration facilities
listed in the 1989 and 1992 CAPs as pending have since been withdrawn. Waste
exports have increased signicantly1 (see Table 1), due in part to the lack of in
state capacity for treating incinerable waste and a hazardous waste fee structure
that encourages out-of-state disposal. The state's 1992 Capacity Assurance Plan
emphasizes California's participation in the Western States Regional Agreement
on Capacity Assurance, a tacit admission of California's continuing dependence on
waste exports.
The state has continued to pursue waste minimization and source reduction as
a way of balancing waste generation and treatment capacity. Funding is provided
for local governments to develop waste minimization programs and to assist small
businesses through loans for implementing waste minimization 35]. Hazardous
waste generators are required to prepare waste management plans that identify
hazardous waste streams and potential source reduction alternatives, formulate a
plan for source reduction, and periodically review it 38]. In 1991, the Department
of Toxic Substance Control initiated a review of these plans from four industry
groups thought to oer the greatest potential for reducing incinerable wastes.
The DTSC promotes waste minimization and source reduction through a series
of industry-specic waste minimization `audit-studies', a waste recycler's catalog,
DSS FOR REGIONAL HAZARDOUS WASTE MANAGEMENT ALTERNATIVES
31
the California Waste Exchange, and a variety of research and outreach eorts.
Many studies, including the department's `Incinerable Hazardous Waste Minimization Project', indicates that large reductions in hazardous waste generation can
be achieved by implementing available pollution prevention and waste reduction
measures.
5. Development of a Decision Support Model
This paper is concerned with developing a model to aid in regional hazardous waste
management planning. The model cannot incorporate all the factors that need to be
considered in regional waste management planning, such fairness or desirability of
waste treatment versus waste reduction. Hence, the model is intended as a support
tool to assess the impact of various policy alternatives rather than as a source of
nal answers.
In section 3.4, we highlighted the fundamental diculties with assuming a complete cooperation between the rms and the Central Authority (CA). It is clear
that the major diculty the CA faces, is dening an objective that would increase
the social benet while satisfying the desire of the rms to maximize their prot.
We attempt to take a step toward a more realistic model of an economy where the
central authority has control over a subset of decision variables (e.g., prices) and
the rms control the other variables (e.g., production).
It is reasonable to assume that the CA has no direct control over such decision
variables as source reduction, or amount of on-site recycling. Rather, it can only
set certain charges, issue permits, or designate a certain capacity for an o-site
facility. This observation split the problem into two: rms and the CA with a
hierarchical structure in which a decision maker (CA) at one level of a hierarchy
may have an objective function and the decision spaces are determined, in part, by
other level (rms). This leads to a model for the operation of a rm as it relates to
waste generation. Given a particular set of prices for osite treatment (including
transportation cost, fees and taxes), what is the rm's demand for osite waste
treatment?
5.1. Risk Assessment
One the most dicult aspect of this decision support model is the assessment of risk
and more specically quantication of risk. In general, emission is caused both by
production activities and treatment methods. These emissions are converted by the
environment into pollution concentration which vary continuously over space and
time. Evaluating the damage these pollution concentrations have had on human
and environment is of particular concern when forming a robust environmental
policy. Risk assessment measures both risk acceptance, or appropriate level of
safety and risk aversion, or methods of avoiding risk that can be used as alternatives
to involuntary exposure. Identifying the risk associated with certain product may
M. AMOUZEGAR AND S. JACOBSEN
32
help in forming policies curbing the production or use of such materials. The risk
assessment should not stop at measuring only the health and life, such as those
resulting in morbidity and premature death, but it should also identify short and
long term environmental and economical impact.
The process of risk evaluation for hazardous waste disposal and treatment greatly
depends on the technology used and the exposure pathway. In particular, in absence
of an alternate technology (e.g., replacing solvent by water-based cleaner) there are
many possible point of hazards. We must evaluate the hazard level during and
after treatment as well as the possible long run risk to the environment from the
disposal of residuals. The treatments and potential hazards points are illustrated
in Figure 1.
Air Pollution
Potential
Hazard
Production
Incineration
Waste Stream Treatment
Little or
No Risk
Technology
Possible
Risk
Recycling
Potential
Hazard
No Risk
Alternative
Technology
Potential Hazard
Disposal
Water/Ground
Pollution
Figure 1. Risk Evaluation for Hazardous Waste Management
Toxicology and epidemiology can provide quantitative data on the relation between the dose(concentration) and response. Several formal and informal methods
are available in estimating a quantitative relationship 28]. In developing a quantitative model we must focus on the quantication of risk in terms of human health.
The precise question is how pollution aect illness and death rates, including partial
DSS FOR REGIONAL HAZARDOUS WASTE MANAGEMENT ALTERNATIVES
33
disability, missed work and expenditures on health. One of the major problems in
attempting to answer these questions is the lack of theoretical model specifying the
way pollution aects health. For example, in terms of air pollution, the predominant eect is more subtle and relates to chronic diseases. Although the principal
eect of air pollution is respiratory diseases, the human body is complex enough so
that other chronic diseases, such as heart disease, are aggravated.
An additional diculty is the methodology used in risk assessment. In particular,
it has been argued (for example, see 27]) that investigating morbidity is more reasonable than examining mortality since death is the end of a complicated sequence
that starts with an initial disease and may evolve in many ways. Unfortunately,
data on morbidity rates, absence rates and health expenditure are not extensively
available. There are, of course, other factors such as Urban living, life style, and
errors in data collection that contribute to computing a damage function.
Adding to an already dicult problem is the fact that with a few notable exceptions, as in the case of asbestos, the determination of human health hazards must
be assessed primarily on the basis of animal studies which are both costly and time
consuming. Some specic sample costs and testing methodologies are presented in
a report for the Oce of Pesticides and Toxic Substances 12].
In our development of a decision support system, we will rely on developing a conceptual damage function that can be set by policy makers according to availability
of data. Accordingly let ( ) denote pollution concentration from production, recycling and incineration. Because our only use of pollution concentration information
is as an argument in pollution damage function, the specic nature of is governed by the damage function, (). Therefore, if pollution damage is a function
of annual average or annual maximum concentration in a region, the can be one
dimensional. If, however, is a nonlinear function of concentration at all points
in a region or regions over all points in time during a year, the will be a nite
approximation to those concentrations.
5.2. Hierarchical Decision Making
The central authority, in order to encourage source reduction, may adopt a policy
of rewarding rms for each unit of source reduction beyond some lower limit set
by the CA. At the same time, the CA desires to punish rms who fail to meet the
minimum source reduction standard and for shipping hazardous waste to osite
incinerators. The rms, of course, incur other cost other than the penalty (tax) set
by the CA. The rms, in planning their waste management policy, need to consider
such costs as the onsite recycling cost (including the setup and operating costs) and
osite recycling and incineration costs. Notationally, let x denote the quantity
of waste type w, w = 1 : : : W , rm i, i = 1 : : : I , sends for onsite recycling, and
similarly let u and v denote the quantity of osite recycling and incineration of
waste type w produced by rm i and shipped to region r, r = 1 : : : R, respectively.
Recycling processes leave certain quantity of residual which need to be incinerated.
Therefore, let , i = 1 : : : I , w = 1 : : : W , denote the fraction of residual from
iw
iwr
iw
iwr
M. AMOUZEGAR AND S. JACOBSEN
34
onsite recycling, and let denote the fraction of residual from osite recycling.
The per unit costs of onsite recycling, osite recycling and osite incineration are
denoted by c , RC and IC , respectively. The total cost to each rm is therefore
denoted by
wr
iw
TC =
rw
X
i
rw
c x + RC u
iw
iw
rw
iwr
+ IC ( x + u
rw
iw
iw
wr
iwr
+ v )]
iwr
r w
P
Let s = x + r ( u + v ) denote the total waste w earmarked for
incineration by rm i and let L denotes the lower bound set by the CA for the
waste type w for each rm i. The CA may attempt to encourage the reduction of
s by setting up a tax/reward system. For example, it may tax each rm for any
value of s > 0, or may reward each rm for source reduction by paying an amount
for each unit of L
s . Notationally, let denote the per unit price CA is
paying each rm for reduction of waste type w, and let denote the per unit tax
the CA levies against rms who generate beyond the lower limit set by law. It may
be that this tax/reward strategy could only be applied to a certain waste type. Let
# be a set of wastes eligible for tax/reward scheme. Benet to each rm is then
iw
iw
iw
wr
iwr
iwr
iw
iw
iw
;
iw
w
w
B (s w ) = ((LL
iw
i
;
w
iw
w
;
iw
s ) if L
s ) if L
;
iw
iw
iw
;
iw
s
0
s >0
iw
iw
Therefore the lower level objective function is expressed as follows
min
X
i
TCi
;
X
w2
Biw (siw )
!
Firms are constrained by the capacity of each of the facilities available to them,
any environmental laws on source reduction, and other physical constraints. In a
decision support model, we can assume a xed quantity of waste generated at the
initial iteration and then revised this quantity to play dierent scenarios of waste
reduction goals. If we denote the initial quantity of waste w generated by each rm
as q then each rm has the following constraint
iw
X
r
u
iwr
+v ]+x
iwr
iw
q
iw
A exible model should not mandate the existence of on- and osite facilities,
rather the solution to the optimization should indicate the need for such facilities.
Let cap denote the possible capacity of an onsite recycling, and let Cap and CAPr
denote the osite recycling and incineration capacities in region r respectively. Then
the three capacity constraints are as follows
i
r
DSS FOR REGIONAL HAZARDOUS WASTE MANAGEMENT ALTERNATIVES
X
iw
cap y
u
iwr
Cap z
+v ]
CAP t
w
X
iw
X
iw
x + u
iw
iw
wr
iwr
x
iwr
i
for all i
i
r
for all r
r
r
35
r
for all r
where y , z and t are the binary decision variables.
The upper level (the central authority) has its own objective to optimize. It is
conceivable that the central authority may wish to minimize the total waste treatment costs and pollution damage cost incurred to the region through the necessity
of meeting some predetermined source reduction standard. These costs include
both the local(on-site) treatment cost function f( ), regional recycling and treatment cost functions ( ) and ( ), respectively and the premium cost p. Thus, the
upper level objective function can be expressed as follows
i
r
r
H
min
p
L
X
X
X
f (x ) +
( u )
wr
iw
i
X
X
x + u + v ]) + ()
wr (
iw
Hwr
iw
L
wr
iw
i
iw
iwr
wr
iwr
iwr
where () denote the pollution damage cost.
5.3. Social Welfare Model
Our second model is to maximize the social welfare of the region and is based partly
on Kolstad's (24]) air pollution control model. One way of dealing with social
welfare is by the idea of economic surplus for the region. Let's dene the economic
surplus ES, in the absence of environmental regulation as the integral under all
inverse demand functions from zero up to consumption level less producers' cost.
ES (g q) =
n Z g
X
P^i ()d Ci (gi qi )
i
i=1
0
;
(1)
where P^i () is the inverse demand function and Ci (gi qi ) is the i-th producer's cost
with gi and qi = (qi1 : : : qiW ) denoting the output level and the vector of waste
quantity respectively.
The role of the CA is to choose a regulation so that when rms respond to the
regulation, social welfare is maximized. One such welfare is dened as economic
surplus (1) less pollution damage. Therefore the CA's objective is to choose a
regulation that maximizes welfare.
M. AMOUZEGAR AND S. JACOBSEN
36
W = ES (g q) ():
(2)
In promulgating a regulation, r, output levels, g(r) and q(r) will be determined
by the market in response to the regulation r. Let the prot function PF for each
rm be dened as revenue minus cost where cost may include regulatory charges.
;
max PF
q u v satisfy r
X
u + v ] + x
q
r
X
(L2)
x
cap y for all i
w
X
u
Cap z for all r
iw
X
x + u + v ] CAP t
iw
iwr
iwr
iwr
iw
iwr
i
iw
iw
i
iwr
r
iw
iw
wr
iw
r
iwr
iwr
r
r
for all r
and the CA optimization model is to seek a regulation r, within a set of feasible
regulations R, which maximizes welfare, given the manner in which the economy
response to such regulations (L2). Then the CA's problem is to
max
W (r)
r 2R
where the value of W is dened by r indirectly through the optimization problem
of the rms (i.e., (L2)).
Consider two types of emission regulations: emission fees and marketable emission
permits. We assume both regulations are set before the rms have made their
production decisions.
1. Emission Fee:
We may either impose an emission fee on all the hazardous wastes generated or
just on those wastes that are send for incineration. (L2) is modied to account
for the imposition of a fee on all hazardous waste at the source or a fee for
lack of source reduction.
2
3
X
Maximize 4PF t
q 5
;
or,
iw
(3)
iw
2
3
X
Maximize 4PF +
B (s )5
iw2
iw
iw
(4)
DSS FOR REGIONAL HAZARDOUS WASTE MANAGEMENT ALTERNATIVES
37
Equation (3) refers to charging all hazardous wastes generated, and equation
(4) refers to previously dened partial charges and incentive.
2. Marketable emission permits:
We may simulate the action of a marketable permit system through a constraint
on (L2). Let Mw be the issuance of emission permits then we may append the
following to the constraint set of (L2)
n
X
i=1
q
iw
Mw w W
(5)
2
Permit trading may be assumed to occur over the entire economy as in equation
(5) or trading may occur only within zones (regions).
5.4. A Brief Note on Centralized Planning
The task of developing a full decision support model requires that we consider the
instances where cooperations between the central authority and the rms may be
possible. Consequently, we present brief descriptions of microeconomic model as
well as a system optimization model that may be useful at certain instances of
policy making.
Our st model considers the problem from the point-of-view of the rms where
as before in a given geographical region many rms operate and produce certain
amount of goods which are not necessarily identical. As a by product these rms'
activities a certain quantity of hazardous waste is generated which need to be
managed.
Let g, denote the output level of a rm which uses factors of production z1 : : : zJ .
Let pj , j = 1 : : : J , denote the per unit price of factor j and let (z ) denote the
rm's production function, where z = (z1 : : : zJ ). Let P (g) denote the rm's
inverse demand function for its product (i.e., P (g) is the per unit price consumers
will pay for a total of g units). Let q(z ) = (q1 (z ) : : : qw (z )) where w W denote
the vector of resulting hazardous wastes. In this model rms may manage their
waste using on-site and o-site facilities, as well as having waste minimization as
an additional option. The usual concept of `waste minimization', at its initial state,
is that the rm may have a few alternatives with respect to the nature of the very
technology that the rm may use to produce its output. We proceed, formally, to
model this important aspect as follows. Let there be T technologies, indexed by
t = 1 : : : T , available to the rm and let t , t = 1 : : : T , denote the corresponding
production functions. Let t = 1 denote the technology the rm is currently using
to produce its output. Assume also that only one technology may be used by the
rm. Denote
technology t is used, and
yt = 10 IfOtherwise
2
M. AMOUZEGAR AND S. JACOBSEN
38
and let T1t denote the cost of switching from the current technology to another
technology denoted by t, t = 2 : : : T . Let qt (z ), t = 1 : : : T denote the rm's
waste vector when using technology t.
In this conceptual framework, the objective of all rms is to maximize the revenue
minus the productions cost, change of technology cost, pollution damage cost and
the operating cost (TC).
max
X
i2I
Pi (gi ) gi
;
XX
i2I j 2J
pij zij
;
XX
i2I t2T
T1it yit ()
;
;
X
i2I
TCi
The constraint set is same as the model of section 5.2 with an addition of the
production constraint
T
X
t=1
it (z i ) yit gi 0:
;
The second model is a simple system optimization model where the problem is
approached from the point-of-view of the central authority. In this area of waste
management where there is a total cooperation between rms and the central authority, the CA is in the control of all the location and allocation decisions.
P This
approach will try to minimize the total cost to the system (i.e., minimize i2I TCi )
given the capacity constraints for all the on- and o-site facilities. In this model,
the optimal solution, if exists, will dictate the behavior of each rm, even though
such optimal solution may not be optimal for a particular rm. Therefore, two very
important questions come to mind, who owns these facilities? And how does the
CA distribute the costs eciently?
We don't allow the sale of excess capacity between the rms, so each on-site facility
is owned and paid for by the corresponding rm. It is in the o-site facilities where
the ownership question arises. One scenario is cooperative ownership by all the
users (rms), another is the ownership by the CA. The third option is a private
ownership. In the rst two scenarios, the cost functions are the set-up cost plus the
operating cost distributed `eciently' between the rms. In the latter scenario a
closer attention, is needed.
If the o-site facilities are owned privately but are fully controlled by the CA, it
would be the same as the CA operating these facilities. Therefore, we must assume
that after the CA has decided on the size, number and the location of the facilities,
it will allow `outside' operation and ownership of these potential facilities through
some sort of allocation system such as marketable permit system. These permits
may incorporate two types of operating systems, private (i.e., allow some type of
prot maximization) or public (i.e., zero prot scheme).
Now, whether we employ the marginal revenue equal marginal cost rule (prot
maximization), price equal average cost rule under economies-of-scale or price equal
marginal cost rule under diseconomies-of-scale (public utility), we are faced with
the diculties of computing accurate demands for these o-site facilities, since the
DSS FOR REGIONAL HAZARDOUS WASTE MANAGEMENT ALTERNATIVES
39
o-site cost functions are no longer the set-up cost plus operating cost. The new
o-site cost functions are just the per unit prices charged by these facilities. It is
immediate that rms' demand for the o-site facilities depends on the o-site prices
which in turn depends on the demands by the rms. It is unrealistic and inadvisable
for the CA to set arbitrary prices (hence the reason for the bilevel programming
model) and then adjust these prices as the o-site facilities respond. The building
and planning of such facilities, alone, take years and the rms' production decisions
may not be so easily changed.
To remedy this cyclical problem, we must assume a full capacity use of each
potential facility. We must further assume that each facility is chosen from a discrete
set of facility sizes (an assumption that is more true to reality). We may then
compute the per unit prices which maximizes the potential owner's prot for each
facility size.
In the case of public utility, we set the price equal the average cost under economiesof-scale or price equal the marginal cost under diseconomies-of-scale with a full
capacity operation. In the case of a prot maximizing industry, the CA must have
some knowledge of these industries revenue functions. Currently, operating facilities may give some indication of desired prot margins, or the permit issuing CA
may set a ceiling on the prot margin (e.g., 10% above cost).
If all the cost functions are convex, the problem becomes `trivial' in the sense
of Generalized Bender's Decomposition 13] where the decision variables of the
constraint set are partitioned into a discrete variable space and the continuous
variable space.
The diculty, beyond the large size of the problem, is where there is an economiesof-scale in play. It is reasonable to assume that in some of these facilities the
marginal cost may decrease as more quantity of waste is sent to them which yield
a nonconvex optimization problem. The diculty with this type of problem is that
current solution techniques may not be able to nd the global (optimal) solution
to the problem. The nonconvexity combined with integer variables, which create
a discontinuous feasible region, will make the problem even more dicult to solve.
Yet, it is exactly this economies-of-scale in the o-site facilities that makes the
model more realistic, and in certain cases it is to each rm's benet to pool their
undesirable products together in order to get a `cheaper' per unit cost.
As we have mentioned earlier this model is appropriate when the decisions are
centralized. In this model the o-site facilities play the role of the suppliers and
the rms have some xed demand. The prices for the o-site facilities depend on
the dierent types of ownership scenarios and the benet function derived from
these scenarios. A benet measure would be the revenue in a private industry,
but in a public facility the is measured by adding to the revenue the additional
benet accruing to consumers from receiving a price lower than the maximum they
would be willing to pay. In another word the gross benet to the society is just the
`willingness-to-pay'.
Let
M. AMOUZEGAR AND S. JACOBSEN
40
P (u v) be the joint inverse demand function for recycling and incineration respectively.
We can mathematically state the benet to a private and public industries as
follows:
1. Private:
For a private enterprise the gross benets are from the revenues, thus the private
benet is
B (u v) = R(u v) = P (u v) (u + v):
(6)
2. Social benet:
For a social enterprise, we dene total benet as the consumers' `willingness to
pay' plus the producers revenue. Suppose for the incremental unit added to a
demand of 1 < u and 2 < v, the `willingness-to-pay' is the price P (
1 2 ) and
therefore the consumers' surplus is
S (u v) =
=
Zu Zv
Zu Zv
0
0
0
0
P (
1 2 ) P (u v)] d
1 d
2
;
P (
1 2 )d
1 d
2 R(u v)
;
and the total social benet is just consumers' surplus plus revenue,
B (u v) = S (u v) + R(u v) =
Zu Zv
0
0
P (
1 2 )d
1 d
2 :
(7)
Now we can introduce a model that considers the benet to all rms and at the
same time regards the pollution damage and the benets to the region. It is easy
to see that the goal of the CA is to maximize the net benet, but the diculty is
whose benet should the CA consider?
It is clear that under any pricing scenario the monetary benet to the o-site
facility is a cost to the rms, and thus the o-site benets and the rms' benets
are not additive. Therefore, our attempt should be to try to maximize the rms'
revenue (benet) minus the on-site, o-site and the pollution damage cost. Of
course, the o-site costs are just the per unit prices set by the o-site facilities
under dierent ownership scenarios of equations (6) and (7).
DSS FOR REGIONAL HAZARDOUS WASTE MANAGEMENT ALTERNATIVES
41
Table 2. Hazardous Waste Generation and Capacity for ABAG Coun-
ties(Tons)
Hazardous Waste Generation
County
1988
Alameda
97,502
Contra Costa 65,306
Marin
1,993
Napa
1,200
San Francisco 44,167
San Mateo
69,645
Santa Clara
92,449
Solano
14,668
Sonoma
7,603
Total
394,533
1989
89,599
95,172
3.253
1,801
64,679
90,919
83,804
25,108
8,743
462,808
1990
86,400
135,287
2,983
1,323
50,787
113,828
95,308
38,587
36,108
560,611
1991
88,282
63,733
3,463
1,663
39,551
114,983
111,041
32,049
8,648
463,413
Treatment
Capacity
80,520
0
2,430
0
76,000
78,900
68,773
0
0
306,643
Waste generation computed from summary tapes of Hazardous
Waste Manifest Data from Department of Toxic Substances Control 26].
Source:
6. Application to the San Francisco Bay Area
Our models have been implemented, for a limited set of waste streams (see Appendix A.1), using San Francisco Bay area as a case study. The nine counties of
this region, which form the Association of Bay Area Governments (ABAG), account
for over 25% of the waste generated in California. Table 2 shows the total osite
disposal of hazardous wastes and current treatment capacity in each county.
The current implementation focuses on incinerable wastes, due to the acute shortage of treatment capacity for them and the limited number of treatment and disposal options. The model includes:
20 dierent waste types, based on California waste codes.
Options for waste management are on- and o-site recycling and incineration,
plus two disposal options for the residuals.
Osite facilities in three discrete sizes.
Capital and operating costs are given for each type and size of facility, based
on an EPA studies 10], 11]
Transportation costs are based on mileage, using the distance between the centers of the counties as average distances, and a cost of $0:23/ton-mile.
Waste generation data for each waste type in each ABAG county, computed
from the `Tanner tapes' of DTSC's Hazardous Waste Information System.
Waste generation in each county is divided among small, medium and large
rms, with the assumption that they account for 20, 30 and 50%, respectively,
of the total generation of each waste type.
42
M. AMOUZEGAR AND S. JACOBSEN
Conceptually, the decision support model will consider the regional hazardous
waste problem and depending on the desire of the policy makers and/or the availability of the information partition the problem into centralized or decentralized
planning (see Figure 2). Many solution techniques and commercial softwares are
available for the linear or the convex optimization formulations of the centralized
planning. Appendix A.2 illustrates an example of a system model using GAMS 6]
modeling language. One of the basic results of this model has been the dominance
of the transportation costs. Further studies is war ranted and is underway. In
case of nonconvex optimization problems (i.e., presence of economies-of-scale in
the objective), there are less choices and specialized programs must be developed.
For more detailed description of these technique see a monograph by Horst and
Tuy 20].
If it is desired to develop optimal taxing or pricing scheme, we must formulate
the problem as a hierarchical model. In the case of the linear upper (i.e., CA)
objective and the linear lower (i.e., rms) objective, there are half a dozen algorithms with varying degrees of success (e.g., see Bard and Moore 3], Hansen et.
al. 18], Amouzegar and Moshirvaziri 2]). To the best of our knowledge, they can
handle about 100 leader variables and 100 follower variables and 50 constraints.
When discrete variables are added, the manageable problem size shrinks by nearly
an order of magnitude. In case of nonlinear objectives, only a few algorithms exist
(e.g., see Vicente and Calamai 44]) but they can only handle small size problems.
Naturally, any nal analysis depends on the political and physical considerations.
7. Summary and Remarks
We have developed a decision support model in order to aid policy makers in developing a sound managerial decision regarding an important issue facing many
industrialized nations. This paper gives a brief history of methods developed in the
area of environmental economics including recent attempts in using optimization
techniques. In this paper, we have recognized the interaction between the central
player and the others by developing a hierarchical model that deals with setting optimal taxing schemes. Issues such as social welfare, risk assessment and cooperation
with rms are also addressed.
A single level model (i.e., where the CA controls all decision variables) is implemented in GAMS, a modeling and optimization package which enables a concise
algebraic description of complex mathematical programming models. The current
implementation contains more than 150 000 continuous variables and 300 binary
variables. Due to the size of the problem, a smaller Hierarchical model is implemented using the algorithm developed by Amouzegar and Moshirvaziri 2]. This
algorithm has been coded on Matlab using the subroutines developed in 33]. Unlike linear or even integer programming problems where we are able to solve very
large scale problems, bilevel models need to be scaled down due to their inherent
complexities. Hence the development of a decision support system where we are
more concerned with a model that can interact with a decision maker.
DSS FOR REGIONAL HAZARDOUS WASTE MANAGEMENT ALTERNATIVES
43
Hazardous Waste
Management Problem
Centralized
Decentralized
Planning
Planning
Production
No
No
Functions
Known?
Yes
Linear
Objectives?
System
Model
Yes
Firms
Model
Linear
Approximation?
Yes
Penalty Method
Branch & Bound
NO
Traditional
Linear/Nonlinear
Heuristics
Branch & Bound
Techniques
Political and Physical Considerations and Feedback
Figure 2. Decision Support Flow Chart
Notes
1. Sources: `Tanner Tapes' of the California Hazardous Waste Information System (HWIS) plus
data from the Out-of-State Manifest System (OSMA), obtained from the Department of Toxic
Substances Control.
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:
M. AMOUZEGAR AND S. JACOBSEN
46
Appendix
A.1. Waste Streams
This appendix presents the 20 types of waste streams used in this paper. The
numbers are the California Waste Category identication numbers.
Waste Group
Recyclable:
Halogenated Solvents
Non-Halogenated
Solvents
California Waste Category
211 Halogenated Solvents
741 Liquids with Halogen
(Org. Comp. > 1000 mg/l)
212 Oxygenated Solvents
213 Hydrogen Solvents
214 Unspecied Solvent Mixtures
Oily Sludges
222 Oil/Water Separation Sludge
Waste oil
221 Waste Oil and Mixed Oil
223 Unspecied Oil Containing Waste
Non-recyclable
Organic Liquid
133 Aqueous with Total Organics > 10%
134 Aqueous with Total Organics < 10%
341 Organic (Non-solvents) Liquids
with Halogens
342 Organic Liquids with Metal
343 Unspecied Organic Liquids Mixture
Halogenated Organic
Sludges and Solids
251 Still Bottoms with Halogenated Organics
351 organic Solids with Halogens
451 Degreasing Sludge
Non-Halogenated Organic 241 Tank Bottom Waste
Sludges and Solids
252 Other Still Bottom Waste
Dye and Paint Sludges
and Resins
Miscellaneous Wastes
271 Organic Monomer Waste
331 O-Spec, Aged or Surplus Organics
A.2. Data Structure
This appendix describes the data used in the system formulation of the problem.
DSS FOR REGIONAL HAZARDOUS WASTE MANAGEMENT ALTERNATIVES
47
sets
I
The nine ABAG regions /region1*region9/
F
Different size firms /fs,fm,fl/
R
Different size recycler /rs,rm,rl/
D
Different size incinerator /incin1*incin3/
*
To simplify we will only consider landfill as an option
*
with three different size to build.
*
Also due to geographical limitation and political considerations
*
only region 1 and 5 can have a landfill.
DS Disposal sites location /DS1, DS5/
DT Different size of disposal sites /DT1*DT3/
*
*
DT1
Landfill
*
DT2
Land Treatment
*
DT3
Waste Pile
*
DT4
Disposal Surface Impoundments
*
DT5
Storage Surface Impoundments
WS
20 waste streams /ws1*ws20/
*
Waste generated by each region ton/year
TABLE A(ws,i) table of waste produced by each region
1
2
ws1
726.5
95.5
ws2
33.4
8.0
ws3
809.5
89.6
ws4
2184.0
96.2
ws5
2627.9 725.0
ws6 19494.7 5889.7
ws7
2602.4 4615.3
125.2
59.2
ws8
ws9
538.4 675.6
ws10
1.1
1.9
ws11
7.9
.6
ws12
250.6 847.8
ws13
429.5 2778.9
ws14
54.9 640.2
ws15
7.7
12.3
ws16
4.5
7.0
ws17 1617.9 934.4
ws18
15.3
0.0
ws19
48.0
7.4
ws20
118.2
70.5
3
4
7.5 0.7
0.0 0.0
8.0 8.2
14.0 0.5
44.7 13.9
85.9 49.6
14.6 3.4
0.0 1.5
7.1 65.9
0.0 0.0
0.0 0.0
1.2 0.2
32.5 0.0
49.8 0.0
0.0 0.0
0.0 0.0
33.7 2.4
0.0 0.0
0.0 0.0
1.0 0.0
5
6
7
8
9
17.0
171.6 1950.0
45.7 258.9
1.3
1.0
13.7
76.2
0.0
33.3
214.6 3326.6
21.2
37.2
87.8
32.5 1642.0
8.2 1659.1
467.3 10123.6 6423.0 175.7
68.6
1045.8 47243.1 12672.0 1982.9 675.7
922.5
119.4 1259.7 1159.7 141.6
21.2
58.9
204.1
0.0
4.8
1376.7
602.9
577.5
38.9
52.7
0.0
.2
50.1
0.0
0.0
1.2
0.0
29.8
0.0
0.9
58.4
244.4
487.4
27.2
52.9
236.5
70.1
329.3 1129.8
8.8
0.0
0.5
4.4
0.0
0.0
0.8
0.0
33.9
0.0
0.0
0.2
1.1
7.2
0.0
0.0
887.1 1686.5
568.9 161.2 125.6
1.3
1.5
2.6
0.0
0.0
1.3
0.1
56.3
2.7
0.0
26.0
15.5
59.9
35.8
0.4
M. AMOUZEGAR AND S. JACOBSEN
48
* Recycling capacities for small, medium and large
*
TABLE Rcap(f,r) table of capacity of recyclers at firm f
rs
rm
rl
fs
1000
0
0
fm
1000
3000
0
fl
1000
3000
8000
* distance between the regions, computed from the center
* of one region to another.
TABLE M(i,j) distance between the counties
1
2
3
4
5
6
7
8
1
0
20
50
50
30
30
30
50
2
20
0
50
50
30
50
50
30
3
50
50
0
30
20
50
80
50
0
50
80
100
30
4
50
50
30
5
30
30
20
50
0
30
50
60
6
30
50
50
80
30
0
30
70
7
30
50
80
100
50
30
0
80
8
50
30
50
30
60
80
80
0
9
100
80
30
30
60
80
140
60
9
100
80
30
30
60
80
140
60
0
*
incineration prices, average cost prices from the third-third
*
report.
*
Parameter cost(d)
/
incin1
incin2
incin3
1.944
1.234
1.033
/
* convert the cost function form $/gallon to $/ton
* 238.09524 gallon = 1 ton.
*
parameter Icost(d) cost for incineration option dollar per ton
Icost(d) = cost(d) * 238.09524
* Disposal cost from the third-third report
Parameter cost2(dt) cost for disposal sites dollar per gallon
/
dt1 2.5
dt2 2.1
DSS FOR REGIONAL HAZARDOUS WASTE MANAGEMENT ALTERNATIVES
dt3
49
1.9/
* convert the cost function form $/gallon to $/ton
parameter Dcost(dt) cost for disposal option dollar per ton
Dcost(dt) = cost2(dt) * 238.09524
* we have assumed three types of firms with certain percentage
* contribution to the waste generation.
parameter Firm(ws,i,f) amount of waste w at firm size f at region i
Firm(ws,i,'fs')= .2*waste(w,i)
Firm(ws,i,'fm')= .3*waste(w,i)
Firm(ws,i,'fl')= .5*waste(w,i)
parameter FR(r) cost of building recycler size r
FR('rs')= 5000
FR('rm')= 9000
FR('rl')= 35000
parameter FI(d) cost of building incineration type d
FI('incin1')= 37000000
FI('incin2')= 49300000
FI('incin3')= 108000000
parameter FD(dt) cost of building disposal site of size dt
FD('dt1')= 100000
FD('dt2')= 150000
FD('dt3')= 250000
Parameter
Ocap(r) capacity of off-site recycler
Ocap('rl')=10000
Parameter Setup(r) setup cost of off-site recycler
Setup('rl')=50000
Parameter Charge(r) per unit charge for off-site recycler
Charge('rl')=270
parameter
Icap(d) capacity
Icap('incin1') =
Icap('incin2') =
Icap('incin3') =
of incinerator at k type t size d
120000
170000
400000
parameter Dcap(dt) capacity of disposal site at k type dt
Dcap('dt1')= 25000
M. AMOUZEGAR AND S. JACOBSEN
50
Dcap('dt2')= 35000
Dcap('dt3')= 50000
parameter Rcost(w,r) cost of recovery of wastes using size r
Rcost(w,'rs')$(ord(w) le 5)= 450
Rcost(w,'rm')$(ord(w) le 5)= 400
Rcost(w,'rl')$(ord(w) le 5)= 260
parameter TC(i,j)
transportation cost
TC(i,j) = M(i,j)*.23
parameter TR(i,ds) transportation cost for residual
TR(i,'ds1')= M(i,'1')* .28
TR(i,'ds5')= M(i,'5')* .28